Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

Graph the function $f$ by starting with the graph of $y = x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.
$f (x) = (x - 3)^{2} - 10$

The required graph is shown below:

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given function is:

$f (x) = (x - 3)^{2} - 10$

Step 2. Determine the transformations used.

In the function $f (x) = a (x - h)^{2} + k, a$ is a constant and $(h, k)$ is the vertex.

In the given function $a = 1, h = 3, k = - 10$ . It means the graph of the given function is a parabola that opens up and has its vertex at $(3, - 10)$ and its axis of symmetry is the line $x = 3$ .

The graph of $y = x^{2}$ shifts 3 units right and 10 units down.

First plot the graph of $y = x^{2}$ then shift it 3 units right and then shift the resulted graph 10 units down to get the graph of the function $f (x) = (x - 3)^{2} - 10$ .

Step 3. Draw the graph.

The required graph is shown below:

Using a graphing utility, we get a graph that is the same as the above graph.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Graph the function $f$ by starting with the graph of $y = x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.
$f (x) = (x - 3)^{2} - 10$

Step by Step Solution

Step 1. Given information.

Step 2. Determine the transformations used.

Step 3. Draw the graph.

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

Graph the function f by starting with the graph of y=x2 and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.f(x)=(x-3)2-10

Step by Step Solution

Step 1. Given information.

Step 2. Determine the transformations used.

Step 3. Draw the graph.

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Graph the function $f$ by starting with the graph of $y = x^{2}$ and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.
$f (x) = (x - 3)^{2} - 10$